Examples of Distributions
and Descriptive Graphs

Frequency Histogram

Discrete values of categories are
used on the horizontal (x) axis, and the number of scores that fall into that
category (i.e., frequency) appears on the vertical (y) axis. A normal curve is overlaid so that one can
easily see how it departs from normal.
This distribution looks close to normal, although there is a pretty high
peak in the middle and a some high frequencies in the right and left tails.

Box Plots

Below are box plots or sometimes
called “box and whiskers.” The center
line is the median, the top and bottom of the box is the upper and lower “hinge”
(approximately the upper and lower quartiles), and the endpoints of the
whiskers represent the approximate range.
SPSS will sometimes print “outliers” and “extreme points” (denoted by circles
and asterisks) that lay outside the end of the whiskers, in which case the
whiskers are not really the lowest and highest scores. Defining an outliers and extreme points is
rather subjective. SPSS uses z-scores greater than a certain value to define
these. However, identifying outlying
points is probably best left to the researcher to define—you may want to
consider some points outliers even though SPSS does not or SPSS may identify
something as extreme that you do not.
Box plots are probably the most useful when you are comparing two
groups.

Stem and Leaf

The Stem and Leaf combines a histogram with actual data
points. If you imagine turning the figure on its side, it resembles a frequency
histogram. The “stems” are categories
for the scores, usually identified by the first digit of the score, and the “leaves”
are the last digit of the score. Often,
some type of rounding is used, depending on whether there are decimals or the
number of digits is large. The
intention is to allow you to identify exact scores in the figure and also get a
sense of the shape of the distribution.

High School GPA
Scores Stem-and-Leaf Plot for

GENDER= Men

Frequency
Stem & Leaf

6.00 1 . 011123

8.00 1 . 56778889

9.00 2 . 000112222

9.00 2 . 555556668

3.00 3 . 023

5.00 3 . 55788

6.00 4 . 000000

Stem width: 1.00

Each leaf: 1 case(s)

High School GPA
Scores Stem-and-Leaf Plot for

GENDER= Women

Frequency
Stem & Leaf

8.00 1 . 01233334

3.00 1 . 699

6.00 2 . 000134

13.00 2 . 5556666779999

8.00 3 . 00011112

4.00 3 . 5789

2.00 4 . 00

Stem width: 1.00

Each leaf: 1 case(s)